Classical evolutionary approaches for multiobjective optimization are quite effective but incur a lot of queries to the objectives; this can be prohibitive when objectives are expensive oracles. A sample-efficient approach to solving multiobjective optimization is via Gaussian process (GP) surrogates and Bayesian optimization (BO). Multiobjective Bayesian optimization (MOBO) involves the construction of an acquisition function which is optimized to acquire new observation candidates. This ``inner'' optimization can be hard due to various reasons: acquisition functions being nonconvex, nondifferentiable and/or unavailable in analytical form; the success of MOBO heavily relies on this inner optimization. We do away with this hard acquisition function optimization step and propose a simple, but effective, Thompson sampling based approach ($q\texttt{POTS}$) where new candidate(s) are chosen from the Pareto frontier of random GP posterior sample paths obtained by solving a much cheaper multiobjective optimization problem. To further improve computational tractability in higher dimensions we propose an automated active set of candidates selection combined with a Nystr\"{o}m approximation. Our approach applies to arbitrary GP prior assumptions and demonstrates strong empirical performance over the state of the art, both in terms of accuracy and computational efficiency, on synthetic as well as real-world experiments.

翻译：古典多目标优化中的进化方法虽然效果显著，但需要大量目标函数查询；当目标函数成本高昂时，这种需求可能难以承受。一种基于高斯过程代理模型和贝叶斯优化的样本高效方法可用于求解多目标优化问题。多目标贝叶斯优化需要构造采集函数，并通过优化该函数获取新的观测候选点。由于采集函数可能非凸、不可微或缺乏解析形式，这种"内部"优化往往面临困难，而MOBO的成功高度依赖于该内部优化过程。我们摒弃了这种复杂的采集函数优化步骤，提出了一种简单但有效的基于汤普森采样的方法（$q\texttt{POTS}$），该方法通过求解一个更廉价的多目标优化问题，从随机GP后验样本路径的Pareto前沿中选择新候选点。为提升高维场景的计算可行性，我们进一步提出结合Nyström近似的自动候选集选取策略。该方法适用于任意GP先验假设，在合成实验和实际实验中均展现出优于现有技术的准确性与计算效率。